Question

The Hamptons Home of a Famed Socialite Hits the Market

“Before there was Paris Hilton, there was Consuelo Vanderbilt Balsan – a Gilded Age heiress and socialite, renowned for her beauty and wealth. Ms. Balsan’s onetime Hamptons home was slated to hit the market priced at $28 million with Tim Davis of the Corcoran Group.

Located on Ox Pasture Road in Southampton, the shingle-style home was built around 1910 and is known as “Gardenside” or “Cara-Mia”. Ms. Balsan, the great-granddaughter of railroad magnate Cornelius Vanderbilt, owned the house until her death in 1954.

According to public records, the estate is owned by Robert G. Goldstein, executive vice president and president of global gaming operations at Las Vegas Sands Corp, and his wife Sheryl, who purchased the house in 2002 for $17.4 million.” (The Wall Street Journal, August 1, 2014, M2)

In your initial response to the topic you have to answer all questions.

1.Calculate the annual compound growth rate of the house price during the period when the house was owned by Robert G. Goldstein (since 2002). (Round the number of years to the whole number). Please show your work.

2.Assume that the growth rate you calculated in question #1 remains the same for the next 30 years. Calculate the price of the house in 30 years after it was sold by Robert G. Goldstein. Please show your work.

3.Assume that the growth rate you calculated in question #1 remains the same since the house was sold. Calculate the price of the house today. (Round the number of years to the whole number). Please show your work.

4.Assume the growth rate that you calculated in #1 prevailed since 1910. Calculate the price of the house in 1910. Please show your work.

5.Assume the growth rate that you calculated in #1 prevailed since 1910. Calculate the price of the house in 1954. Please show your work.

6.You were using the time value of money concept to answer question #5. Think about the time line for that problem. What is the time point 0 in that problem? Please explain your answer.

Answer 1

1. Annual Compound Growth rate = ((Ending value/Beginning Value)^(1/no. of years))-1

Here Ending value is $28M, Beginning value is $17.4M, No. of years will be from 2002 to 2014 i.e 12 years

=((28/17.4)^(1/12))1 =4.04%

2. Price of house after 30 Years will be= Price in 2002*(1+growth rate)^no of years

=17.4*(1+0.0404)^30 =$57.16M

3. Price of house today will be 16 Years i.e from 2002 to 2018 will be= Price in 2002*(1+growth rate)^no of years

=17.4*(1+0.0404)^16 =$32.81M

4. No.of years from 1910 to 2002 will be 92 Years. At the growth rate of 4.04% its value reach to $17.4M in 2002

Value in 1910= Value in 2002/(1+r)^no. of years

= 17.4/(1.0404)^92=$0.45 M

5. From the Question 4 we got the value in 1910 i.e$0.45M and no of years from 1910 to 1954 will be 44 Years

So value in 1954 = Value in 1910*(1+r)^no. of years

= 0.45*(1.0404^44) =$2.59M

6 Time Point Zero will be starting point of the time line , since in question 5 we started from 1910 and calculated the value in 1954 . Time Point Zero will be 1910.